bkm7: Optimal Risky Portfolios Flashcards
Portfolio Risk & equation for equally weighted assets
total variance of portfolio
Systemic risk portion of portfolio risk
Covariance because this equation will approach this as n goes to ∞
Efficient diversification
lowest risk level for a given return
expected return and variance of return for 2 risky assets
if correlation is less than 1
portfolio can be constructed that has lower variance than portfolio with single asset
Minimum variance portfolio
portfolio with lowest variance that can be constructed from assets with a certain level of correlation, this is different than optimal portfolio
minimum variance portfolio will consist of both D&E if […]
& min variance portfolio will consist of exclusively of D when
- ρ<σD/σE
- if 1 is not true, will consist of D (lower variance asset) because no benefit to diversification, invest all in lower variance
Portfolio opportunity set
plots return as function of std deviation for 2 risky assets for a given correlation
each curve in below graph for given correlation (plot of expected return vs std dev of portfolio that depends on w and correlation)
min var portfolio is not
optimal portfolio
CAL(A)=consisting of risk free and min variance portfolio A
can construct CAL(B) with risk free and alternate portfolio B with steeper slope aka higher Sharpe ratio that also intersects portfolio opportunity set
Optimal risky portfolio
available portfolio that has highest Sharpe-> portfolio where CAL is tangential to portfolio opportunity set
contains only risky assets which is in contrast to optimal complete portfolio
Tangency portfolio
portfolio with CAL tangential to portfolio opportunity set
wD formula for tangency portfolio
once optimal risky portfolio weights have been calculated, optimal complete portfolio can be constructed
depends on level of risk aversion
Calculate y, then proportions in D, E, and risk free
Minimum-Variance Frontier
portfolios that have lowest variance of each level of expected return
Global Min-Var Portfolio:
single portfolio with lowest variance
-investor should invest along frontier and no reason investor should select portfolio below global because top ½ have same risk with higher return
Efficient Frontier:
top ½ of min-var frontier
Optimal complete portfolio
expected return and variance of return
consists of a risk-free asset and an optimal risky asset portfolio
Separation principle:
2 steps in portfolio selection = selection of optimal risky portfolio and allocation between risk free vs risky assets and this will depend on level of risk aversion
-in reality optimal risky can vary between clients due to their unique portfolio constraints -> efficient frontier subject to constraints will have Sharpe ratio that is inferior
Risk pooling:
merging several uncorrelated projects together -> selling many uncorrelated insurance policies
- authors argue risk pooling alone actually increases total exposure to risk
- as investor increases risk pooling, both Sharpe and std deviation will increase by n^0.5
- insurer will need to hold more capital to protect against greater risk
Risk sharing:
sharing fixed amount of risk among several investors
- higher Sharpe ratio achieved from risk pooling without having to increasing exposure to risk
- can reduce risk by selling shares of insurer to investors -> Sharpe ratio will rise as number of policies increase but risk to each shareholder falls
Investment for Long Run
- people believe that extending investments across time will reduce risk
- can think of extending investment horizon to be same as adding additional risky asset to pool
- extending the time horizon increases the Sharpe ratio but std dev will be higher
